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<div class="subTitle">org.apache.commons.math3.linear</div>
<h2 title="Class RRQRDecomposition" class="title">Class RRQRDecomposition</h2>
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<pre>public class <span class="strong">RRQRDecomposition</span>
extends <a href="../../../../../org/apache/commons/math3/linear/QRDecomposition.html" title="class in org.apache.commons.math3.linear">QRDecomposition</a></pre>
<div class="block">Calculates the rank-revealing QR-decomposition of a matrix, with column pivoting.
 <p>The rank-revealing QR-decomposition of a matrix A consists of three matrices Q,
 R and P such that AP=QR.  Q is orthogonal (Q<sup>T</sup>Q = I), and R is upper triangular.
 If A is m&times;n, Q is m&times;m and R is m&times;n and P is n&times;n.</p>
 <p>QR decomposition with column pivoting produces a rank-revealing QR
 decomposition and the <a href="../../../../../org/apache/commons/math3/linear/RRQRDecomposition.html#getRank(double)"><code>getRank(double)</code></a> method may be used to return the rank of the
 input matrix A.</p>
 <p>This class compute the decomposition using Householder reflectors.</p>
 <p>For efficiency purposes, the decomposition in packed form is transposed.
 This allows inner loop to iterate inside rows, which is much more cache-efficient
 in Java.</p>
 <p>This class is based on the class with similar name from the
 <a href="http://math.nist.gov/javanumerics/jama/">JAMA</a> library, with the
 following changes:</p>
 <ul>
   <li>a <a href="../../../../../org/apache/commons/math3/linear/QRDecomposition.html#getQT()"><code>getQT</code></a> method has been added,</li>
   <li>the <code>solve</code> and <code>isFullRank</code> methods have been replaced
   by a <a href="../../../../../org/apache/commons/math3/linear/RRQRDecomposition.html#getSolver()"><code>getSolver</code></a> method and the equivalent methods
   provided by the returned <a href="../../../../../org/apache/commons/math3/linear/DecompositionSolver.html" title="interface in org.apache.commons.math3.linear"><code>DecompositionSolver</code></a>.</li>
 </ul></div>
<dl><dt><span class="strong">Since:</span></dt>
  <dd>3.2</dd>
<dt><span class="strong">Version:</span></dt>
  <dd>$Id: RRQRDecomposition.java 1570994 2014-02-23 11:10:41Z luc $</dd>
<dt><span class="strong">See Also:</span></dt><dd><a href="http://mathworld.wolfram.com/QRDecomposition.html">MathWorld</a>, 
<a href="http://en.wikipedia.org/wiki/QR_decomposition">Wikipedia</a></dd></dl>
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<td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/linear/RRQRDecomposition.html#RRQRDecomposition(org.apache.commons.math3.linear.RealMatrix)">RRQRDecomposition</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;matrix)</code>
<div class="block">Calculates the QR-decomposition of the given matrix.</div>
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<td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/linear/RRQRDecomposition.html#RRQRDecomposition(org.apache.commons.math3.linear.RealMatrix, double)">RRQRDecomposition</a></strong>(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;matrix,
                 double&nbsp;threshold)</code>
<div class="block">Calculates the QR-decomposition of the given matrix.</div>
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<td class="colFirst"><code>protected void</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/RRQRDecomposition.html#decompose(double[][])">decompose</a></strong>(double[][]&nbsp;qrt)</code>
<div class="block">Decompose matrix.</div>
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<tr class="rowColor">
<td class="colFirst"><code><a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/RRQRDecomposition.html#getP()">getP</a></strong>()</code>
<div class="block">Returns the pivot matrix, P, used in the QR Decomposition of matrix A such that AP = QR.</div>
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<td class="colFirst"><code>int</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/RRQRDecomposition.html#getRank(double)">getRank</a></strong>(double&nbsp;dropThreshold)</code>
<div class="block">Return the effective numerical matrix rank.</div>
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<tr class="rowColor">
<td class="colFirst"><code><a href="../../../../../org/apache/commons/math3/linear/DecompositionSolver.html" title="interface in org.apache.commons.math3.linear">DecompositionSolver</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/RRQRDecomposition.html#getSolver()">getSolver</a></strong>()</code>
<div class="block">Get a solver for finding the A &times; X = B solution in least square sense.</div>
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<td class="colFirst"><code>protected void</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/linear/RRQRDecomposition.html#performHouseholderReflection(int, double[][])">performHouseholderReflection</a></strong>(int&nbsp;minor,
                            double[][]&nbsp;qrt)</code>
<div class="block">Perform Householder reflection for a minor A(minor, minor) of A.</div>
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<h3>Methods inherited from class&nbsp;org.apache.commons.math3.linear.<a href="../../../../../org/apache/commons/math3/linear/QRDecomposition.html" title="class in org.apache.commons.math3.linear">QRDecomposition</a></h3>
<code><a href="../../../../../org/apache/commons/math3/linear/QRDecomposition.html#getH()">getH</a>, <a href="../../../../../org/apache/commons/math3/linear/QRDecomposition.html#getQ()">getQ</a>, <a href="../../../../../org/apache/commons/math3/linear/QRDecomposition.html#getQT()">getQT</a>, <a href="../../../../../org/apache/commons/math3/linear/QRDecomposition.html#getR()">getR</a></code></li>
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<pre>public&nbsp;RRQRDecomposition(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;matrix)</pre>
<div class="block">Calculates the QR-decomposition of the given matrix.
 The singularity threshold defaults to zero.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>matrix</code> - The matrix to decompose.</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../org/apache/commons/math3/linear/RRQRDecomposition.html#RRQRDecomposition(org.apache.commons.math3.linear.RealMatrix, double)"><code>RRQRDecomposition(RealMatrix, double)</code></a></dd></dl>
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<pre>public&nbsp;RRQRDecomposition(<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;matrix,
                 double&nbsp;threshold)</pre>
<div class="block">Calculates the QR-decomposition of the given matrix.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>matrix</code> - The matrix to decompose.</dd><dd><code>threshold</code> - Singularity threshold.</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../org/apache/commons/math3/linear/RRQRDecomposition.html#RRQRDecomposition(org.apache.commons.math3.linear.RealMatrix)"><code>RRQRDecomposition(RealMatrix)</code></a></dd></dl>
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<h4>decompose</h4>
<pre>protected&nbsp;void&nbsp;decompose(double[][]&nbsp;qrt)</pre>
<div class="block">Decompose matrix.</div>
<dl>
<dt><strong>Overrides:</strong></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/linear/QRDecomposition.html#decompose(double[][])">decompose</a></code>&nbsp;in class&nbsp;<code><a href="../../../../../org/apache/commons/math3/linear/QRDecomposition.html" title="class in org.apache.commons.math3.linear">QRDecomposition</a></code></dd>
<dt><span class="strong">Parameters:</span></dt><dd><code>qrt</code> - transposed matrix</dd></dl>
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<pre>protected&nbsp;void&nbsp;performHouseholderReflection(int&nbsp;minor,
                                double[][]&nbsp;qrt)</pre>
<div class="block">Perform Householder reflection for a minor A(minor, minor) of A.</div>
<dl>
<dt><strong>Overrides:</strong></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/linear/QRDecomposition.html#performHouseholderReflection(int, double[][])">performHouseholderReflection</a></code>&nbsp;in class&nbsp;<code><a href="../../../../../org/apache/commons/math3/linear/QRDecomposition.html" title="class in org.apache.commons.math3.linear">QRDecomposition</a></code></dd>
<dt><span class="strong">Parameters:</span></dt><dd><code>minor</code> - minor index</dd><dd><code>qrt</code> - transposed matrix</dd></dl>
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<h4>getP</h4>
<pre>public&nbsp;<a href="../../../../../org/apache/commons/math3/linear/RealMatrix.html" title="interface in org.apache.commons.math3.linear">RealMatrix</a>&nbsp;getP()</pre>
<div class="block">Returns the pivot matrix, P, used in the QR Decomposition of matrix A such that AP = QR.

 If no pivoting is used in this decomposition then P is equal to the identity matrix.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>a permutation matrix.</dd></dl>
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<h4>getRank</h4>
<pre>public&nbsp;int&nbsp;getRank(double&nbsp;dropThreshold)</pre>
<div class="block">Return the effective numerical matrix rank.
 <p>The effective numerical rank is the number of non-negligible
 singular values.</p>
 <p>This implementation looks at Frobenius norms of the sequence of
 bottom right submatrices.  When a large fall in norm is seen,
 the rank is returned. The drop is computed as:</p>
 <pre>
   (thisNorm/lastNorm) * rNorm < dropThreshold
 </pre>
 <p>
 where thisNorm is the Frobenius norm of the current submatrix,
 lastNorm is the Frobenius norm of the previous submatrix,
 rNorm is is the Frobenius norm of the complete matrix
 </p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>dropThreshold</code> - threshold triggering rank computation</dd>
<dt><span class="strong">Returns:</span></dt><dd>effective numerical matrix rank</dd></dl>
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<h4>getSolver</h4>
<pre>public&nbsp;<a href="../../../../../org/apache/commons/math3/linear/DecompositionSolver.html" title="interface in org.apache.commons.math3.linear">DecompositionSolver</a>&nbsp;getSolver()</pre>
<div class="block">Get a solver for finding the A &times; X = B solution in least square sense.
 <p>
 Least Square sense means a solver can be computed for an overdetermined system,
 (i.e. a system with more equations than unknowns, which corresponds to a tall A
 matrix with more rows than columns). In any case, if the matrix is singular
 within the tolerance set at <a href="../../../../../org/apache/commons/math3/linear/RRQRDecomposition.html#RRQRDecomposition(org.apache.commons.math3.linear.RealMatrix, double)"><code>construction</code></a>, an error will be triggered when
 the <a href="../../../../../org/apache/commons/math3/linear/DecompositionSolver.html#solve(org.apache.commons.math3.linear.RealVector)"><code>solve</code></a> method will be called.
 </p></div>
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<dt><strong>Overrides:</strong></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/linear/QRDecomposition.html#getSolver()">getSolver</a></code>&nbsp;in class&nbsp;<code><a href="../../../../../org/apache/commons/math3/linear/QRDecomposition.html" title="class in org.apache.commons.math3.linear">QRDecomposition</a></code></dd>
<dt><span class="strong">Returns:</span></dt><dd>a solver</dd></dl>
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